Academic journal article The Journal of Developing Areas

Long Memory and Arfima Modelling: The Case of CPI Inflation Rate in Ghana

Academic journal article The Journal of Developing Areas

Long Memory and Arfima Modelling: The Case of CPI Inflation Rate in Ghana

Article excerpt

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INTRODUCTION

In macroeconomic theory and economic policy, changes in the general price level or the rate of inflation plays an essential role. Hence, for example, one of the motives behind the adoption of Inflation Targeting policy (IT) by Ghana and the treaty espoused by the European Monetary Union, known as the Maastricht Treaty, was the convergence of inflation rates. Moreover, the last two decades of macro and financial economic research has resulted in a huge collection of important contributions in the area of long memory modelling, both from a theoretical and an empirical standpoint. From a theoretical perspective, considerable effort has been focussed in the areas of testing and estimation, and a few significant contributions include Granger (1980), Granger and Joyeux (1980), Hosking (1981), Geweke and Porter-Hudak (1983), Lo (1991), Sowell (1992a), Ding et al. (1993), Cheung and Diebold (1994), Robinson (1994; 1995a,b), etc. The empirical analysis of long memory models also has seen equally remarkable treatment, including studies by Diebold and Rudebusch (1989, 1991a,b), Hassler and Wolters (1995), Gil-Alana and Robinson (1997), Hyung and Franses (2001), Bos et al. (2002). Indeed, the considerable array of publications on the subject is not surprising, given the importance of long memory models in economics following the seminal contributions made by Clive W.J. Granger (see e.g. Granger (1980).

We have seen that a significant number of the analyses of financial time series and econometrics hinge on the assumption of an efficient market hypothesis (henceforth EMH), which in its weak form states that returns of variables such as inflation rates, exchange rates, interest rates, equity prices among others, are expected to be i.i.d. white noise. This means, they follow the martingale process, hence not predictable (Fama, 1970). Notwithstanding the countless number of research papers following the pioneering work of Nelson and Plosser (1982), differences still remain in the literature on the main question of whether or not the post-war inflation possesses a unit root. Even though there is substantial evidence backing the unit root process (e.g. Barsky, 1987; MacDonald and Murphy, 1989; Ball and Cecchetti, 1990; Wickens and Tzavalis, 1992; and Kim 1993), Rose (1988) provided evidence of stationarity in inflation rates. Mixed evidence has been provided by Kirchgassner and Wolters (1993) whereas Brunner and Hess (1993) argued that the inflation rate was stationary before the 1960s, but that it possesses a unit root since then.

A probable resolution to this debate should not only be of academic interest, as nonstationarity in inflation would have dire consequences for central banks' ratification of inflationary shocks with its ripple effect on the macroeconomic policymakers' response to external pressures. A breakthrough to the challenge of this conflicting evidence was recently provided by modelling inflation rates through fractionally integrated processes. Using fractional differentiation and ARFIMA models, Baillie et al. (1996) examined a group of seven countries (UK, USA, Italy, France, Germany, Canada and Japan), and found strong evidence of long memory in the inflation rates with the exception of Japan. Comparable evidence of long memory in inflation rates of the USA, the UK, Germany, France and Italy is also provided by Hassler and Wolters (1995). Delgado and Robinson (1994) found evidence of long memory in the Spanish inflation rates. The clarification of this evidence put forward that inflation rates are mean-reverting processes and that inflationary shock will persist but ultimately dissipate.

A time series exhibits long memory when there is significant dependence between observations that are separated by a long period of time. Characteristics of a long memory time series are an autocorrelation function ( ) that decays hyperbolically to zero and a spectral density function (. …

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